Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

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1answer
35 views

How to compute for a sequence for a given value in wolfram?

What would be the correct input in the wolfram website to give u(n) for a given n, where u is a sequence ? Something like: ...
2
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1answer
49 views

Calculating the 1st quartile: different result with Excel, Wolfram Alpha and using formula in my math book - why?

I have the following set of numbers: 1, 1, 8, 12, 13, 13, 14, 16, 19, 22, 27, 28, 31 I'm supposed to calculate the value of the 1st quartile (25th percentile) in this data set. Using the formula in ...
3
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1answer
58 views

Solving an integral with limits of polygamma functions

I've been trying to solve the following integral: $$I_n=\int_0^1\frac1x\ln^n(x)\ln^{8-n}(1-x)~\mathrm dx$$ for $n\in[2,6]$. It can be computed as a limit of derivatives of the Beta function: $$I_n=\...
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2answers
61 views

Wolfram Alpha can plot an equation but not solve it

I'm trying to solve the equation $24.6347 \left(246.347 x + \sqrt{(246.347 x + 20)^2 + 1} + 20\right)^{-a} =\\ 30.2879 \left(-33.6532 x + \sqrt{x (1132.54 x - 20191.9) + 90001} + 300\right)^{-a}$ ...
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2answers
49 views

Why does WolframAlpha omit the $n=4$ and $n=8$ term in this Fourier series?

I tried to determine the Fourier series of the function: $$ f(x) = \begin{cases} x+\pi, & -\pi \le x < -\frac{\pi}{2} \\ \frac{\pi}{2}, & -\frac{\pi}{2} \le x <\frac{\pi}{2} \\ \pi-x, ...
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2answers
65 views

How do I solve a recurrence relation with multiple conditions?

Suppose I have a recurrence relation like : \begin{equation} f(n)=\begin{cases} 2*f(n-1) , & \text{n%2 = 1}.\\ f(n-1) + 1, & \text{n%2 = 0}. \end{cases} \end{equation} \begin{...
2
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0answers
61 views

Wrong Wolfram alpha result on $nth$ derivative?

I'm working with this function $$f(x)=\left(x+\sqrt{x^2-a}\right)^{-b}$$ and I would like to know the $nth$ derivative of $f(x)$. To this end, I ask Wolfram alpha about that given me the following ...
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1answer
35 views

Is there some technique to plot complex functions by hand?

Is there some technique to plot complex functions by hand? Particularly, consider e.g. $$x=\exp(t)\cos(t), y=\exp(t)\sin(t)$$ This is equivalent to $e^x(\cos(y)+i\sin(y))$ along line $y=x$, just ...
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0answers
30 views

Why do these Residues and Numerically Calculated Contour Integrals Disagree?

I've been trying to numerically approximate various contour integrals of the function $f(z)=\frac{\sin\left(\pi x\right)}{\sin^2\left(\frac{15\pi}{x}\right)}$, but it seems that the residues and ...
2
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1answer
103 views

A bug in Wolfram Alpha about an infinite series?

While verifying this MSE answer, I may have come across a bug in Wolfram Alpha. It evaluates the sum below as, $$\qquad A=\sum_{n=0}^\infty\frac{\binom{2n}{n}^2}{16^n(n+1)^3}=1.03928049\color{red}{51}...
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0answers
48 views

Plot a graph with a hole in Wolfram Alpha

I would like to emphasize graphs with holes in Wolfram alpha, so I've tried graphing a rational function with a hole. However, the graph that WA is generating isn't showing the hole. Is there a way to ...
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1answer
38 views

How does one plot $z=(-2)^{3/5}$?

How does one plot $z=(-2)^{3/5}$? I see in Wolfram Alpha: https://www.wolframalpha.com/input/?i=z%5E5%3D-8 But I don't understand how that plot is created.
1
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1answer
47 views

3D plot difference Matlab and Wolfram

I'm trying to plot the function $z = 6x^2 - 4x^2y^2$ in Matlab. The code I'm using for this in matlab is the one below, also the plot is shown: ...
2
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1answer
44 views

FFT from scilab is different than wolfram alpha [closed]

I am getting completely different values of FFT([1,2]) in scilab and Wolfram. I wondering what is going on and who is right. ...
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0answers
20 views

Numerical Double Integration with inverse over inner integral failing using common methods and inbuilt functions

Implementing a paper, I want the value of this double integral which has endpoint singularities in both integrals. $\int_0^{\inf} \frac{1}{w} Im( 0.5^{-iw}({12{\int_0^1 (1 - (0.5+\frac{0.5} {1+by^\...
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2answers
35 views

Why “is $f(x)$ an odd function?” does not work with this function?

We know that $f(x)$ is odd if $-f(x)=f(-x)$. The function is $$f(x)=\begin{cases}2x-1&\text{if $-2<x<0$},\\2x+1&\text{if $0\leq x\leq2$}.\end{cases}$$ (link) Now I want to know if $f$ ...
2
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2answers
44 views

Infinite sum and partial sum not equal in Wolframalpha

$$\sum_{n=0}^{\infty} |(-0.8)^n \theta(n)-(-0.8)^{n-1} \theta(n-1)|$$ $\theta(n) = 1$ for $n \geq 0$ and 0 otherwise. My attempt to calculate this summation numerically with Python yielded 10. To ...
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0answers
25 views

How to plot a Riemann sum in Wolfram alpha

I am wondering if there's a simple way to plot a function with a Riemann sum in Wolfram alpha. I've looked in a bunch of places for a tutorial but can't seem to find one. Anyone wanna help please?
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2answers
48 views

Is Wolfram Alpha wrong? (trig identity)

I have the following identity $$ \sqrt{\cos(2x)\sec^4(x)}$$ I use the property $ \sqrt{a} \sqrt{b} = \sqrt{ab} $ which then yields $$ \sqrt{\cos(2x)} \, \sec^2(x) $$ However, Wolfram tells me ...
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1answer
43 views

How to find coordinates that split this arc into 3 pieces of equal length?

I need the $x$ coordinates of two new points that split an elliptical arc between 2 given points in quadrant I into 3 equal pieces. How can I get these coordinates? I want to use Wolfram but I can ...
2
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1answer
50 views

Different forms of Maclaurin expansion of $f(x,y) = \frac{1}{x+y}$

I am trying to use Taylor series to approximate the value of $f(x,y) = \frac{1}{x+y}$ for some code I am writing. Using WolframAlpha to quickly compute the Maclaurin series gives me: $$ \frac{1}{y} - \...
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0answers
23 views

Calculating an area of parametric function with wolframalpha?

Using wolframalpha, how can I calculate an area between some parametric function like: $\begin{cases} x(t) = t^2 - t \\ y(t) = t^3\end{cases}$ and: some other function like: $y = x^2$ ? I've ...
0
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2answers
57 views

How to find $\frac{146}7 \mod{7}$?

I understand that if $\gcd{(b,c)}=1$ then we can find $\frac{a}b\mod{c}$ by writing $$x\equiv \frac{a}b\mod{c}$$ $$bx\equiv a\mod{c}$$ then reducing $a$ and solving the modular equation by finding the ...
2
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3answers
50 views

How to compute $a\cdot \lim\limits_{n \to \infty}n?$

How to compute $$a\cdot \lim_{n \to \infty}n?$$ I think such an expression is not valid. Though $\lim\limits_{n \to \infty}n=\infty$, which is not a concrete real number, we can not put it into a ...
3
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1answer
153 views

Why wolfram alpha claimed that this $\sum_{n=1}^{\infty}\sin (\frac{n}{\sqrt{n!}}) $ is converge by test and in the same time is diverge?

I'm confused why wolfram alpha claimed that this sum $$\sum_{n=1}^{\infty}\sin \left(\frac{n}{\sqrt{n!}}\right) $$ is convergent by test criterion, and in the same time is divergent in result below ...
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1answer
79 views

Inconsistency of limits

Let $I_n(x)$ and $L_n(x)$ be the modified Bessel and modified Struve functions of order $n$, respectively. Assuming $x$ is real, I am interested in the following limit: $$ \lim_{x\to\infty} \frac{I_0(...
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2answers
39 views

Ability to generate a list of 3-digit numbers from a pool of digits in Wolfram?

I am attempting to generate a list of all possible 3-digit numbers that can be made by the numbers 1, 3, 5, 6, 7 and 9. I believe Wolfram should have the ability to give me a list, however, I am not ...
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2answers
90 views

Integral in Symbolab and WolframAlpha have different results

So Wolfram Alpha and Symbolab have different reuslt for this integral $\int \frac{x}{x+2}dx$. I done it myself and got result like Wolfram Alpha : $x-2\ln|x+2|$. Symbolab display this one: $x+2-2\ln|x+...
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5answers
48 views

Range of function $f(x)=x \sqrt{1-x^2}$

How to find range of this function, it looks easy but somehow I am not able to do that . What is more important to me is , why is wolframalpha unable to find the range , is it not a simple enough ...
1
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2answers
70 views

Are all values of $x$ solutions for $e^{2\ln(\sin(x))} = 1 - e^{2\ln(\cos(x))}$ in $\mathbb R$?

Does all values of $x$ in $\mathbb R$ satisfy equation: $$e^{2\ln(\sin(x))} = 1 - e^{2\ln(\cos(x))}$$ I am asking this, because by checking WolframAlpha solution there is an answer: (all values for $...
0
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1answer
43 views

Solving simple quadratic - Wolfram Alpha confusion?

I have the following quadratic $$(2\sqrt 2 - 2)x^2 + \sqrt8 x + (1+\sqrt 2)=0$$ Now the discriminant of this is $0$, so it has one real repeated root. A plot on Desmos confirms this. However, ...
0
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3answers
70 views

Calculating Fourier series of $\cos^2(t)$ gives unexpected result

As I understand it: $\cos^2(t)$ is even because it is a product of two even functions $\cos(t)$. The Fourier series and Fourier cosine series of an even function is the same link. So in the fourier ...
3
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2answers
128 views

Solving $1^x+2^x+3^x=0$ equations…

Is it possible to solve for x this kind of equation? Since 1,2,3 are not multiples to each other I see a priori no possibility. $$1^x+2^x+3^x=0; x?$$ Computing this on Wolfram Alpha, for example, ...
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2answers
77 views

Simple Differential Equation in Matlab and Wolfram get two different answer?

I'm a beginner in using Matlab. if I have a DE like $$x'(t)=\frac{1}{\sin (2x)}$$ How I can Implement in Matlab to calculate just answer? I try dsolve like as: ySol(t) = dsolve(ode,cond) but ...
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1answer
47 views

Wrong wolframalpha result, calculating Carmichael number?

I put to wolframalpha $3^{560}\pmod{561}$ and result should be $1$ ($561$ is Carmichael number), but result is $375.$ https://www.wolframalpha.com/input/?i=3%5E560mod561 Why this happens? I found ...
0
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1answer
64 views

How to make Wolfram Alpha give me a range of possible answers for an equation if the subject is assumed to be an integer?

I am trying to use Wolfram Alpha, and I am trying to get it to give me a range of possible answers for y=(391-x)/x, if y was an integer. However, there are two problems I face with this. The first is ...
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1answer
67 views

Prove that $\sum_{i=1}^n \frac{1}{\sqrt i} < 2 \sqrt n$ by induction - result doesn't match to wolfram alpha's result

According to wolfram alpha, this inequality isn't true for $n > 2$. My result says otherwise. Assuming that the inequality is true for $n+1$, $\sum_{i=1}^{n+1} \frac{1}{\sqrt i} < 2 \sqrt {n+1}...
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0answers
26 views

Wolfram Mathematica input form of conditional probability

I heard that the conditional probability form of Wolfram Mathematica is like this: Probability[x < 1 \[Conditioned] ....... However, what is Mathematica input form of double conditioned. For ...
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1answer
35 views

Wolfram Alpha - FourierParameters not working with discrete fourier transform

I am trying to calculate the discrete fourier transform using the signal processing convention. The documentation gives the followng example: ...
2
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0answers
164 views

How can I compute a fourier series with Wolfram alpha?

How can I compute the Fourier series of a function on a interval using Wolfram ? For example, the Fourier of $f(x)=x^2$ on $[0,2\pi]$ prolonged on $\mathbb R$ by $2\pi$ periodicity. For example, if I ...
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2answers
65 views

Is there supposed to be a difference between $x^{1/3}$ and $\sqrt[3]{x}$ ? (Wolfram Alpha shows different results)

Compare these two functions: plot $\sqrt[3]{x}$ and plot $x^{1/3}$ I understand how roots are ambiguous, and Wolfram Alpha apparently takes the principle root with the $x^{1/3}$ case and the real ...
3
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2answers
333 views

Can I conclude that $\lim_{x\to0^+}\frac{x^2}{e^{-\frac{1}{x^2}}\cos(\frac{1}{x^2})^2}$ is infinite or it doesn't exists?

$$\lim_{x\to0^+}\frac{x^2}{e^{-\frac{1}{x^2}}\cos(\frac{1}{x^2})^2}$$ My intuition is that the denominator goes to 0 faster and everything is non-negative, so the limit is positive infinity. I cant ...
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0answers
19 views

The first principal subresultant coefficient of two polynomials

Let $f=f(x), g=g(x) \in \mathbb{C}[x]$, with $\deg(f)=\deg(g)=n \geq 2$. Write $f=(x-a_1)\cdots(x-a_n)$ and $g=(x-b_1)\cdots(x-b_n)$, where $a_i,b_i \in \mathbb{C}$, $1 \leq i \leq n$. Let $\lambda,\...
0
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0answers
35 views

Computing subresultants in WolframAlpha

Let $f(x)=(x-a_1)(x-a_2)\cdots(x-a_m)$ and $g(x)=(x-a_{m+1})(x-a_{m+2})\cdots(x-a_n)$, where $m,n \in \mathbb{N}$, $m < n$, $a_i \in F$, $F$ is a field of characteristic zero (for example, $k \in \{...
3
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2answers
77 views

Calculating value of $\text{sinc}(x)$, WolframAlpha and MATLAB give two different answers.

I need to evaluate the following: $$\frac{2}{3}\text{sinc}\bigg(\frac{2\pi}{3}(n-4)\bigg)-\frac{1}{3}\text{sinc}\bigg(\frac{\pi}{3}(n-4)\bigg)$$ for $n=[0,...,8]$ I don't have the sinc function in ...
1
vote
1answer
52 views

What is the meaning of a limit as $e^{(n+1) \infty}$ in WolframAlpha?

I inputted the following into WolframAlpha: lim x to 0 of (cotx)/x^n And I got $$\lim_{x \rightarrow 0}{\frac{\cot{x}}{x^n}} = e^{(n+1) \infty}$$ What does ...
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2answers
76 views

If $q \neq 5$ or $k \neq 1$, do the following conditions follow?

This is a follow-up to MSE question #2998091. From that question, we were able to get the bounds $$\frac{q-1}{q(q+1)} = f(1) \leq f(k) < \frac{q-2}{q(q-1)}$$ and $$0 < f(q) \leq f(5) = \frac{(5^...
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0answers
75 views

How to generate interpolating polynomial using Newton formula for exponential function?

I am trying to find interpolating polynomial of $f(x) = e^{3x}$ and interpolation nodes $x_0=x_1=x_2 = 0\ and\ x_3 = x_4 = 1 $ with Newton's formula using Wolfram Alpha, but I am stuck with division ...
3
votes
1answer
94 views

Why does Wolfram Alpha give $\sum_{n=1}^{\infty}(e^i)^{n^2}\approx9.92988+1.76807i$?

When I input $$\sum_{n=1}^{\infty}(e^i)^{n^2}$$ in Wolfram Alpha, it gives me the result, $$\sum_{n=1}^{\infty}(e^i)^{n^2}\approx9.92988+1.76807i$$ I think this is wrong, but I do not understand why ...
1
vote
1answer
107 views

Global extrema for $\frac{(q^k-1)(q^{k+1}-2q^k+1)}{{q^k}(q-1)(q^{k+1}-1)}$?

Does the function $$\frac{(q^k-1)(q^{k+1}-2q^k+1)}{{q^k}(q-1)(q^{k+1}-1)}$$ have either a global minimum or a global maximum for $q \geq 5$ and $k \geq 1$? WolframAlpha is unable to find any. ...